Question

The rate constant of a reaction is $1.5\times 10^7{s}^{-1}$ at $50^{\circ }C$ and $4.5\times 10^7{s}^{-1}$ at $100^{\circ }C$. What is the value of activation energy?

• A. $2.2\times 10^{3}Jmo{l}^{-1}$
• B. $2300Jmo{l}^{-1}$
• C. $2.2\times 10^{4}Jmo{l}^{-1}$
• D. $220Jmo{l}^{-1}$

Answer 1

Answer: (C)

$\log \frac{4.5\times 10^7}{1.5\times 10^7}=\frac{E_a}{2.303\times 8.314}\left[\frac{373-323}{373\times 323}\right]$
$T_1=50+273=323$
$T_2=100+273=373$
$\log 3=\frac{E_a}{2.303\times 8.314}\left[\frac{50}{373\times 323}\right]$
$\frac{0.4770\times 2.303\times 8.314\times 373\times 323}{50}=E_a$
$E_a=22007Jmo{l}^{-1}\approx 2.2\times 10^4$